Method and apparatus for processing video signals using coefficient induced prediction

1. A method of encoding a video signal based on a graph-based lifting transform (GBLT), comprising: detecting an edge from an intra residual signal, wherein a model for the intra residual signal is designed by using a Gaussian Markov Random Field (GMRF); generating a graph based on the edge, wherein the graph comprises a node and a weight link; obtaining a GBLT coefficient by performing the GBLT for the graph; quantizing the GBLT coefficient; and entropy-encoding the quantized GBLT coefficient, wherein the GBLT comprises a split process, a prediction process, and an update process, wherein the split process of the GBLT is performed to minimize a Maximum A Posteriori (MAP) estimate error within a prediction set, and wherein the method further comprises: obtaining a DCT coefficient by performing a DCT on the intra residual signal; comparing a rate-distortion cost of the DCT coefficient with a rate-distortion cost of the GBLT coefficient; determining, based on the rate-distortion cost of the GBLT coefficient being smaller than the rate-distortion cost of the DCT coefficient, a mode index corresponding to the GBLT; and entropy-encoding the mode index.

2. The method of claim 1 , wherein the split process comprises: calculating a size of an update set; selecting a node minimizing an MAP estimate error within a prediction set based on the size of the update set; and calculating an update set for the selected node.

3. The method of claim 1 , wherein the graph is reconnected prior to a next GBLT.

4. A method of decoding a video signal based on a graph-based lifting transform (GBLT), comprising: extracting a mode index indicative of a transform method from the video signal; deriving a transform corresponding to the mode index, wherein the transform indicates one of a DCT and the GBLT; performing an inverse transform for an intra residual signal based on the transform; and generating a reconstructed signal by adding the inverse-transformed intra residual signal to a prediction signal, wherein a model for the intra residual signal is designed by using a Gaussian Markov Random Field (GMRF), wherein the mode index is determined by comparing a rate-distortion cost of a DCT coefficient with a rate-distortion cost of a GBLT coefficient, and wherein a split process of the GBLT is performed to minimize a Maximum A Posteriori (MAP) estimate error within a prediction set.

5. An apparatus for encoding a video signal based on a graph-based lifting transform (GBLT), comprising: a processor configured to: detect an edge from an intra residual signal, wherein a model for the intra residual signal is designed by using a Gaussian Markov Random Field (GMRF); generate a graph based on the detected edge and obtaining a graph-based lifting transform (GBLT) coefficient by performing the GBLT for the graph; quantize the GBLT coefficient; and perform entropy encoding for the quantized GBLT coefficient, wherein the GBLT comprises a split process, a prediction process, and an update process, wherein the split process of the GBLT is performed to minimize a Maximum A Posteriori (MAP) estimate error within a prediction set, and wherein the processor is further configured to: obtain a DCT coefficient by performing a DCT on the intra residual signal; compare a rate-distortion cost of the DCT coefficient with a rate-distortion cost of the GBLT coefficient; determine, based on the rate-distortion cost of the GBLT coefficient being smaller than the rate-distortion cost of the DCT coefficient, a mode index corresponding to the GBLT; and entropy-encode the mode index.

6. An apparatus for decoding a video signal based on a graph-based lifting transform (GBLT), comprising: a processor configured to: extract a mode index indicative of a transform method from the video signal; derive a transform corresponding to the mode index and perform an inverse transform for an intra residual signal based on the transform; and generate a reconstructed signal by adding the inverse-transformed intra residual signal to a prediction signal, wherein a model for the intra residual signal is designed by using a Gaussian Markov Random Field (GMRF), and wherein the transform indicates one of a DCT and the GBLT, wherein the mode index is determined by comparing a rate-distortion cost of a DCT coefficient with a rate-distortion cost of a GBLT coefficient, and wherein a split process of the GBLT is performed to minimize a Maximum A Posteriori (MAP) estimate error within a prediction set.